Arriving into Naples on a Monday (4pm), end of May, and wanting to make the best of my Tues/Wed/Thursday before taking a train North on Friday afternoon. Archeological Museum & Capella Sansevero in Naples, Herculaneum & Pompeii are a must but now have heard that Positano & Sorrento should also be considered. Don't "need" to fit all of this in but open to suggestions. No lodging reservations yet anywhere so am open to staying where it would be most convenient, even if it means a couple of places in 3 days. Train? Bus? Both?
You could do a daytrip from Naples to one of the nearby islands: Capri, Ischia, Procida; (bus or taxi to the port, then a ferry); or go down to the Amalfi Coast (you could stop at Sorrento and Positano on the way to Amalfi; Circumvesuviana commuter train from Naples to Sorrento, then bus to Positano/Amalfi or any other stops - you can get an all-day bus ticket that lets you stop where you want).
Make Sorrento your base and do day trips to all of the other locations. You'll love Sorrento, and its transportion/lodging/ dining options make it a great base. This is covered quite well in Rick's book.